In [1]}, the distribution of the particles \(\lbrace {\theta }^{[i]}_t\rbrace _{i=1}^N\)  in the limit as \(N \rightarrow \infty \)  is given by the mean-field PDE
\(\partial _t \mu _t({\theta }) = - \nabla \cdot \left(\mu _t({\theta }) \mathbb {E}_{{\theta }^{\prime } \sim \mu _t}\left[ K({\theta }^{\prime }, {\theta })\nabla \log \eta ({\theta }^{\prime }) + \nabla _1 K({\theta }^{\prime }, {\theta }) \right] \right)\,,\) 
